[1] M. Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesnik 66 (2014), no. 2, 223—234.
[2] R.P. Agarwal, D. O’Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8 (2007), no. 1, 61—79.
[3] F. Ali, J. Ali and J.J. Nieto, Some observations on generalized non-expansive mappings with an application, Comput. Appl. Math. 39 (2020), no. 2, 1–20.
[4] D. Ariza-Ruiz, C. Hermandez Linares, E. Llorens-Fuster and E. Moreno-Galvez, On α-nonexpansive mappings in Banach spaces, Carpath. J. Math. 32 (2016), 13—28.
[5] K. Aoyama and F. Kohsaka, Fixed point theorem for α-nonexpansive mappings in Banach spaces, Nonlinear Anal. 74 (2011), 4387-–4391.
[6] M. Bachar and M.A. Khamsi, On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces, Fixed Point Theory Appl. 2015 (2015), 160.
[7] V. Berinde, Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, Fixed Point Theory Appl. 2 (2004), 97–105.
[8] G.A. Bocharov and F.A. Rihan, Numerical modelling in biosciences using delay differential equations, J. Comput. Appl. Math. 125 (2000), no. 1–2, 183–199.
[9] G.H. Coman, G. Pavel, I. Rus and I.A. Rus, Introduction in the theory of operational equation, Ed. Dacia, Cluj-Napoca, 1976.
[10] C. Garodia and I. Uddin, A new fixed point algorithm for finding the solution of a delay differential equation, AIMS Math. 5 (2020), no. 4, 3182–3200.
[11] F. Gursoy and V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument, arXiv:1403.2546v2 (2014).
[12] G. H¨ammerlin and K.H. Hoffmann, Numerical mathematics, Springer, Berlin, 1991.
[13] S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc. 4 (1974), no. 1, 147–150.
[14] W.R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–610.
[15] E. Naraghirad, N.C. Wong and J.C. Yao, Approximating fixed points of α-nonexpansive mappings in uniformly convex Banach spaces and CAT(0) spaces, Fixed Point Theory Appl. 2013 (2013), 57.
[16] M.A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251 (2000), 217-–229.
[17] G.A. Okeke and M. Abbas, A solution of delay differential equations via Picard-Krasnoselskii hybrid iterative process, Arab. J. Math. 6 (2017), 21–29.
[18] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591—597.
[19] H. Piri, B. Daraby, S. Rahrovi and M. Ghasemi, Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process, Numer. Algorithms 81 (2019), no. 3, 1129–1148.
[20] F.A. Rihan, D.H. Abdelrahman, F. Al-Maskari, F. Ibrahim and M.A. Abdeen, Delay differential model for tumour immune response with chemoimmunotherapy and optimal control, Computat. Math. Meth. Med. 2014 (2014), Article ID982978, 15 pages.
[21] F.A. Rihan, C. Tunc, S.H. Saker, S. Lakshmanan and R. Rakkiyappan, Applications of delay differential equations in biological systems, Complexity 2018 (2018), Article ID 4584389, 3 pages.
[22] F. Shahin, G. Adrian, P. Mihai and R. Shahram, A comparative study on the convergence rate of some iteration methods involving contractive mappings, Fixed Point Theory Appl. 2015 (2015), no. 1.
[23] Y.S. Song, K. Promluang, P. Kumam and Y.J. Cho, Some convergence theorems of the Mann iteration for monotone α-nonexpansive mappings, Appl. Math. Comput. 287 (2016), 74–82.
[24] B.S. Thakur, D. Thakur and M. Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings, Applied Math. Comput. 275 (2016), 147-–155.
[25] U.E. Udofia, A.E. Ofem and D.I. Igbokwe, Convergence analysis for a new faster four steps iterative algorithm with an application, Open J. Math. Anal. 5 (2021), no. 2, 95–112.
[26] H.K. Xu, Inequality in Banach spaces with applications, Nonlinear Anal. 16 (1991), 1127-–1138.